Chronic heart failure (HF) is a highly prevalent disease associated with high rates of mortality, which have persisted despite recent advances in pharmacologic therapy. Within the VA, outpatient encounters for HF reached 900,000 in FY09 and VA hospitalizations were over 96,000. Central sleep apnea (CSA) is a common comorbid condition, with moderate to severe CSA present in approximately one-third of patients with chronic HF with reduced ejection fraction. Central sleep apnea is associated with a doubling of mortality in chronic HF. Several small treatment trials show improvement in left ventricular ejection fraction (LVEF) following treatment of CSA with continuous positive airway pressure (CPAP) or adaptive pressure-support servo-ventilation (ASV), although the single long-term outcome study of CPAP therapy for CSA in HF found no difference in transplant-free survival despite improved LVEF. Moreover, most HF patients with CSA do not experience typical sleep apnea symptoms and are therefore often unwilling to accept the discomfort of positive airway pressure therapy. Therefore, better tolerated and possibly more effective alternatives to positive airway pressure are needed for treating CSA in patients with chronic HF. Supplemental oxygen during sleep has been shown to reduce the severity of CSA in some patients with chronic HF. Moreover, although the adverse effects of CSA on HF are likely to be multifactorial, the intermittent hypoxia characteristic of sleep apnea appears to play a central role. Hypoxia is the major cause of sympathetic hyperactivity in sleep apnea, which may contribute to progression of myocardial dysfunction through both direct effects on the myocardium and through elevation of blood pressure; it stimulates the generation of reactive oxygen species, which may contribute to myocyte damage and death; and it induces transcription factors that promote systemic inflammation. This suggests that prevention of nocturnal hypoxemia might mitigate the adverse effects of sleep apnea on the heart, even if it does not eliminate CSA per se. This study is a randomized clinical trial to assess the effects of nocturnal supplemental oxygen (NSO), CPAP and ASV for the treatment of CSA in patients with chronic HF with reduced ejection fraction. Patients with chronic HF with LVEF <45% will be screened for CSA with overnight portable sleep monitoring in their own home. A total of 161 patients with moderate to severe CSA, defined as an apnea-hypopnea index >15 with >50% of events being central apneas or hypopneas, will then be randomized in a 1:2:2:2 ratio to 3 months of treatment with optimal medical management alone, optimal medical management plus CPAP, optimal medical management plus ASV, or optimal medical management plus nocturnal supplemental oxygen. The primary outcome measures, to be made at baseline and at the end of the treatment period, will be change in LVEF as measured by echocardiogram and change in peak VO2 as measured by cardiopulmonary exercise testing. Secondary outcome measures will include 24 hour ambulatory blood pressure profile, urinary catecholamine excretion, urinary excretion of isoprostanes (a marker of oxidative stress), aminoterminal propeptide of type III collagen (a marker of ventricular remodeling), B-type natriuretic peptide, and plasma levels of several markers of inflammation. Adherence to therapy with NSO, CPAP and ASV will also be compared. The primary analysis will compare each of the active treatment groups to control. A non-inferiority design will be used to assess whether NSO and CPAP are non-inferior to ASV.